Squaring the circle is impossible...
Squaring the circle - Wikipedia, the free encyclopedia
preface: I don't do math. I sometimes look up things in math and physics, and find things of interest. So, in the case of 'squaring the circle', I had a non-mathematical idea about solving this, in part because it has a 'physical' element: "in a finite number of steps, using a compass and straight edge".
I am assuming both tools are marked with increments/there are some ways to determine length along the straight edge, and radius of compass arm separation.
Given the following figure:
Aren't the cardinal directions and the corners of the circle relative to concentric circles within and outside of the first circle?
Or, another way: aren't the intersections of the square and circle plottable along the diameter?
Squaring the circle is impossible...
Squaring the circle - Wikipedia, the free encyclopedia
No further comment need be made. In Euclidean proofs neither the straightedge nor the compass have markings on them. In fact it is assumed that the compass closes when taken away from the paper. So you can't measure off equal intervals or angles without using a construction.
-Dan
Sorry, those are the rules. See Compass and straightedge constructions - Wikipedia, the free encyclopedia